tree search

Bidirectional Evolutionary Search (BES) for Self-Improving Language Models

BES is a search framework that combines forward evolutionary candidate generation with backward goal decomposition to address limitations of best-of-N and tree search methods. Forward search uses recombination operators to escape the narrow entropy shell of autoregressive expansion, while backward search recursively decomposes tasks into checkable subgoals for dense intermediate feedback. Theoretical analysis shows evolutionary operators can escape entropy-shell confinement and backward search can exponentially reduce required samples. Experiments demonstrate consistent gains on post-training tasks where mainstream algorithms fail, and superior performance on three open problem-solving benchmarks at inference time.